Delft University of Technology
Hybridization Kinetics Explains CRISPR-Cas Off-Targeting Rules
Klein, Misha; Eslami Mosallam, Behrouz; Gonzalez Arroyo, D.W.; Depken, Martin
DOI
10.1016/j.celrep.2018.01.045
Publication date
2018
Document Version
Final published version
Published in
Cell Reports
Citation (APA)
Klein, M., Eslami Mosallam, B., Gonzalez Arroyo, D. W., & Depken, M. (2018). Hybridization Kinetics
Explains CRISPR-Cas Off-Targeting Rules. Cell Reports, 22(6), 1413-1423.
https://doi.org/10.1016/j.celrep.2018.01.045
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Article
Hybridization Kinetics Explains CRISPR-Cas
Off-Targeting Rules
Graphical Abstract
Highlights
d
Physical model shows CRISPR/Argonaute off-targeting rules
to be kinetic in origin
d
Seed region and mismatch-pattern dependence is due to the
kinetics of hybridization
d
Binding is more promiscuous than cleavage due to kinetically
stalled hybridization
d
Engineered systems can increase specificity without losing
on-target efficiency
Authors
Misha Klein, Behrouz Eslami-Mossallam,
Dylan Gonzalez Arroyo, Martin Depken
Correspondence
s.m.depken@tudelft.nl
In Brief
Predicting potential off targets forms an
important part of any gene-editing
technology intended for therapeutic use.
By constructing a kinetic model for target
recognition by RNA-guided nucleases,
Klein et al. explain experimentally
observed off-targeting rules as a direct
consequence of guide-target
hybridization dynamics.
Klein et al., 2018, Cell Reports22, 1413–1423 February 6, 2018ª 2018 The Author(s).
Cell Reports
Article
Hybridization Kinetics Explains
CRISPR-Cas Off-Targeting Rules
Misha Klein,1Behrouz Eslami-Mossallam,1Dylan Gonzalez Arroyo,1,2and Martin Depken1,3,*
1Kavli Institute of NanoScience and Department of BioNanoScience, Delft University of Technology, Delft 2629HZ, the Netherlands 2Present address: Mathematical Institute, Leiden University, 2333CA Leiden, the Netherlands
3Lead Contact
*Correspondence:s.m.depken@tudelft.nl https://doi.org/10.1016/j.celrep.2018.01.045
SUMMARY
Due to their specificity, efficiency, and ease of
programming, CRISPR-associated nucleases are
popular tools for genome editing. On the genomic
scale, these nucleases still show considerable
off-target activity though, posing a serious obstacle to
the development of therapies. Off targeting is often
minimized by choosing especially high-specificity
guide sequences, based on algorithms that codify
empirically determined off-targeting rules. A lack
of mechanistic understanding of these rules has
so far necessitated their
ad hoc implementation,
likely contributing to the limited precision of present
algorithms. To understand the targeting rules, we
kinetically model the physics of guide-target hybrid
formation. Using only four parameters, our model
elucidates the kinetic origin of the experimentally
observed off-targeting rules, thereby rationalizing
the results from both binding and cleavage assays.
We favorably compare our model to published
data from Cas9, Cpf1,
CRISPR-Cascade, as well as the human Argonaute 2 system.
INTRODUCTIONRNA-guided nucleases (RGNs) target nucleic acid sequences based on complementarity to any guide RNA (gRNA) loaded into the complex. This versatility, together with the ability to design synthetic gRNAs complementary to any target of choice, holds great promise for gene-editing and gene-silencing appli-cations (Cox et al., 2015; Tycko et al., 2016). Among the known RGNs, the Cas nucleases Cas9 (Cong et al., 2013; Gasiunas et al., 2012; Jinek et al., 2012; Mali et al., 2013) and Cpf1 (Zetsche et al., 2015) are of special interest, as they are compar-atively simple single-subunit enzymes.
Cas nucleases originate from the CRISPR-Cas adaptive im-mune system, which many prokaryotes use to fight off foreign genetic elements. In vivo, the Cas protein (complex) is pro-grammed by loading RNA transcribed from a CRISPR locus in the host genome. The transcribed sequence includes sections referred to as spacers, which were acquired during past encoun-ters with foreign genetic elements (Wiedenheft et al., 2012).
Once programmed, the Cas nuclease is able to target and degrade genetic elements with the same sequence as the stored spacer and so offers protection against repeat invasions. An autoimmune response to sequences stored at the CRISPR locus is prevented through the additional requirement of a protein-mediated recognition of a short protospacer-adjacent motif (PAM) sequence present in the foreign genome, but not incorpo-rated into the CRISPR locus with the spacer (Anders et al., 2014; Jinek et al., 2012).
As viruses evolve in response to the selective pressure induced by the CRISPR-Cas immune system, the host is in turn under pres-sure to attack slightly mutated target sequences in addition to the target. It is therefore not surprising that Cas nucleases exhibit considerable off-target activity on sequences similar to the in-tended target (Anderson et al., 2015; Fu et al., 2013, 2014a, 2016; Hsu et al., 2013; Kim et al., 2016; Kleinstiver et al., 2016a; Kuscu et al., 2014; O’Geen et al., 2015; Pattanayak et al., 2013; Wu et al., 2014). Such off targeting presents a severe problem for therapeutics, as DNA breaks introduced at the wrong site could lead to loss-of-function mutations in a well-functioning gene or the improper repair of a disease-causing gene (Cox et al., 2015).
To shed light on the determinants of off-target activity, a recent flurry of experiments has probed the level of binding and/or cleavage on mutated target sequences: high-throughput screens of large libraries of off targets (Doench et al., 2016; Fu et al., 2013, 2014a, 2016; Hsu et al., 2013; Pattanayak et al., 2013); genome-wide identification (Cameron et al., 2017; Frock et al., 2015; Kim et al., 2015; Kleinstiver et al., 2016a; Kuscu et al., 2014; Ran et al., 2015; Tsai et al., 2015, 2017; Wu et al., 2014); systematic biochemical studies (Anderson et al., 2015; Cong et al., 2013; Doench et al., 2016; Jinek et al., 2012; Kim et al., 2016; Kleinstiver et al., 2016a; Lin et al., 2014; Ran et al., 2015; Semenova et al., 2011); structural studies (Anders et al., 2014; Jiang et al., 2015, 2016; Jinek et al., 2014; Nishimasu et al., 2014; Xiao et al., 2017; Zhao et al., 2014); and single-mole-cule biophysical studies (Jo et al., 2015; Josephs et al., 2015; Rutkauskas et al., 2015; Salomon et al., 2015; Singh et al., 2016; Sternberg et al., 2014; Szczelkun et al., 2014), providing in-sights into the mechanics of targeting. To date, a number of rather peculiar targeting rules have been empirically established for Cas nucleases: (1) seed region: single mismatches within a PAM proximal seed region can completely disrupt interference (K€unne et al., 2014; Semenova et al., 2011), whereas PAM distal mismatches have much less of an effect (Anderson et al., 2015; Cong et al., 2013; Doench et al., 2016; Fu et al., 2013, 2014a,
Cell Reports 22, 1413–1423, February 6, 2018ª 2018 The Author(s). 1413 This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
2016; Hsu et al., 2013; Jinek et al., 2012; Kim et al., 2016; Klein-stiver et al., 2016a; Kuscu et al., 2014; O’Geen et al., 2015; Pat-tanayak et al., 2013; Rutkauskas et al., 2015; Semenova et al., 2011; Sternberg et al., 2014; Szczelkun et al., 2014; Wu et al., 2014); (2) mismatch spread: when mismatches are outside the seed region, off targets with spread out mismatches are targeted most strongly (Boyle et al., 2017; Fu et al., 2013, 2014a; Hsu et al., 2013); (3) differential binding versus differential cleavage: binding is more tolerant to mismatches then cleavage (Bikard et al., 2013; Dahlman et al., 2015; Duan et al., 2014; Kuscu et al., 2014; O’Geen et al., 2015; Tsai et al., 2015; Wu et al., 2014); (4) specificity-efficiency decoupling: weakened protein-DNA interactions can improve target selectivity while still maintaining efficiency (Kleinstiver et al., 2015a, 2015b, 2016b; Slaymaker et al., 2016). Although these experimental observa-tions have already aided the development of strategies to improve the specificity of the CRISPR-Cas9 system (Fu et al., 2014b; Kleinstiver et al., 2015a, 2016b; Ran et al., 2013; Slay-maker et al., 2016), an understanding of the mechanistic origin behind target selectivity is still lacking, and our ability to predict off targets remains limited (Cameron et al., 2017; Haeussler et al., 2016; Tsai et al., 2015; Tycko et al., 2016).
Current off-target prediction algorithms are often based on sequence alignment with the target and discard potential targets if they have more than some (user-defined) threshold number of mismatches (Bae et al., 2014; Haeussler et al., 2016; Heigwer et al., 2014; Labun et al., 2016). To recover the mismatch-posi-tion dependence observed as seed regions (rule [1]) and their cooperativity (rule [2]), such scoring schemes must be supple-mented with ad hoc rules that penalize seed and closely spaced mismatches more than non-seed mismatches (Doench et al., 2016; Hsu et al., 2013). To move beyond ad hoc scoring schemes, we here use biophysical modeling to incorporate
knowledge of the underlying targeting process. With this aim, it would be attractive to assume that the binding dynamics has had time to equilibrate before DNA degradation (Farasat and Salis, 2016; Khorshid et al., 2013), as this would allow us to use simple binding/hybridization energetics to predict cleavage activity. Though attractive, this approach has recently been questioned byBisaria et al. (2017)by noting that off rates are generally not found to be much faster than cleavage rates, as would be required for establishing a binding equilibrium before cleavage. In addition, the authors show how abandoning the equilibration assumption directly explains the specificity in-crease observed with shortened gRNA (Fu et al., 2014b).
Inspired by these observations, we go beyond binding ener-getics to build a biophysical model capturing the kinetics of guide-target hybrid formation. We show that the targeting rules (1)–(4) can be seen as simple consequences of kinetics. The target-ing rules are captured by four parameters that pertain to transition barriers between metastable states of the nuclease-guide-target complex, and we translate these into four experimentally observ-able quantities: the length of the seed region; the width of the tran-sition region from seed to non-seed; the maximum amount of cleavage on single-mismatch off targets; and the minimal distance between mismatches outside the seed region that allows for the cleavage of targets with multiple mismatches. By tying micro-scopic properties to biological and technological function, we here open the door to refined and rational reengineering of the CRISPR-Cas system to further its use in therapeutic applications. Though we frame our considerations in terms of the well-studied and technologically important Cas9, our approach applies to any RGN that displays a progressive matching between guide and target before cleavage (Figure 1A). To demonstrate the generality and power of our approach, we present fits to targeting data from Argonaute 2 (hAgo2), as well as type I, II, and V CRISPR systems. A
B
Figure 1. Kinetic Model of RGN Target Recognition
(A) The RGN initially binds its substrate at the PAM site, from which it can either unbind with rate kbð0Þ or initiate R-loop formation with rate kfð0Þ. A partially formed
R-loop of length n grows to length n+ 1 with rate kfðnÞ or shrinks to length n 1 with rate kbðnÞ. Eventually, the RGN will either cleave its substrate with rate kfðNÞ or
reject the substrate and unbind with rate kbð0Þ. In the special case of a RGN that does not utilize PAM binding, it is assumed to bind straight into the initial state of
R-loop formation.
(B) The transition landscape of our minimal model. In the left panel, we illustrate a PAM bound enzyme kinetically biased toward R-loop formation by different amounts (black, gray, and light gray curves). The kinetic bias for the canonical PAM is shown as DPAM. In the middle panel, we illustrate two kinetic biases toward
R-loop extension (black and gray curves), with the larger bias indicated as DC. In the same panel, we further illustrate two kinetic biases against R-loop extension
(gray and light gray curves) at mismatches (red vertical lines), with the largest bias shown as DI. Once the complete R-loop is formed, the system is kinetically
biased against cleavage by Dclv
C=I= DclvHDC=I, as dictated by the nature of the terminal base pairing. SeeFigure S1for complete energy landscapes.
RESULTS
At the start of target recognition, Cas nucleases bind to double-stranded DNA (dsDNA) from solution. The subsequent recogni-tion of a PAM sequence triggers the DNA duplex to open up (Figure 1A), exposing the PAM proximal nucleotides to base pair-ing interactions with the guide (Anders et al., 2014; Jiang et al., 2016). From here, an R-loop is formed, expanding the guide-target hybrid in the PAM distal direction (Josephs et al., 2015; Rutkauskas et al., 2015; Semenova et al., 2011; Singh et al., 2016; Szczelkun et al., 2014; Xiao et al., 2017). If the target and guide reach (near-) full pairing, cleavage of the two DNA strands is triggered (Sternberg et al., 2015).
To establish the determinants of off- versus on-target cleav-age, we construct a biophysical model of sequential target recognition in the unsaturated binding regime (Experimental Pro-cedures). Using this model, we can calculate the rate of cleavage for off targets, given the guide. To incorporate the mechanics of hybrid formation, we envision the changing extension of the R-loop as a diffusion through a free-energy landscape, eventu-ally ending in either unbinding from, or degradation of, the targeted sequence (Figures S1A and S1B). Our model is param-eterized by the free energy of transition states surrounding the metastable states of PAM binding and the different progressions of R-loop formation (Experimental Procedures and Supple-mental ExperiSupple-mental Procedures 1). When in a metastable state, the RGN will be biased toward transitioning to the neighboring state with the lowest intervening barrier. The differences in heights of the surrounding barriers thus encode the directions in which the system is most likely to progress, and we therefore refer to these differences as kinetic biases (Figure S1C). The bal-ance between eventual unbinding or cleavage can be calculated with reference to kinetic biases alone and visualized by a ‘‘tran-sition landscape’’ tracing out the tran‘‘tran-sition states (Figures 1B and S1; Experimental Procedures). In such a landscape, the R-loop typically grows whenever the forward barrier is lower than the backward barrier; that is, whenever the transition land-scape tilts downward. To facilitate the discussion of our exact results, we appropriate a rule of thumb from the limit of large biases (Experimental Procedures): after binding the PAM, Cas9 is most likely to unbind before cleavage if the highest barrier to cleavage is greater than the highest barrier to unbinding and vice versa (Figures S1A and S1B).
Though we treat the general scenario in the Experimental Proceduressection, we here further limit ourselves to a mini-mal description with only four effective microscopic parame-ters, pertaining to the average kinetic bias for R-loop initiation after PAM bindingðDPAMÞ, R-loop extension past a correctly
matchedðDCÞ and mismatched ðDIÞ base pairs, and additional
bias against cleavage once the R-loop is fully formed (Dclv;
for definitions, seeFigure 1B andExperimental Procedures). The parameter Dclv is chosen such that the forward barrier
after R-loop completion is independent of the nature of the ter-minal base (Experimental Procedures), setting the final bias against cleavage to Dclv
C=I= DC=IHDclv (Figure 1B). Using this
approach, we investigate to what extent our minimal model explains the four empirical targeting rules deduced from experiments.
Rule (1): Seed Region
Following PAM binding, base pairing between guide and target is attempted (Figure 1B, middle panel). To establish whether the above-mentioned dependence of the cleavage propensity on the position of mismatches within the guide-target hybrid could originate from the kinetics of the targeting process, we calculate the relative cleavage probability on a sequence with a single mismatch at position n compared to the cleavage probability on the target sequence. InSupplemental Experimental Proced-ures 2, we show that this relative cleavage probability is in general sigmoidal
pclvðnÞ =
pmax
1+ exp½ ðn nseedÞDC;
(Equation 1)
with nseed giving the position where the cleavage probability is
half that of its maximum pmax (Figure 2A) and the biases are
measured in units of kBT. We identify nseedas the length of the
kinetic seed region, beyond which a mismatch will no longer strongly suppress cleavage (Figure 2A). FromEquation 1, we see that the width of the transition from seed to non-seed region directly reports on the (average) correct-match bias (DC;
Supple-mental ExperiSupple-mental Procedures 2), becoming narrower as the bias increases (Figures 2A andS2A).
The emergence of a seed-like region can be understood from considering the rule of thumb that the fate of the enzyme is dictated by the largest barrier: when a mismatch is placed at
nseed (Figure 2B, right panel), the highest barrier to cleavage
matches the barrier toward unbinding, guaranteeing a near equal probability for cleavage and unbinding. Placing the mismatch closer to the PAM increases the highest barrier toward cleavage (compare highest node to first node in Figure 2B, left panel), increasing the probability of rejecting such off targets. Moving the mismatch distally from the PAM will gradually lower the high-est barrier toward cleavage (Figure 2B, middle panel), increasing the probability of accepting such off targets. Though the exact form of the parameters ofEquation 1are given in the Supple-mental Information, it is informative to here give the kinetic seed length in the large-bias limit (Experimental Procedures;
Supplemental Experimental Procedures 2),
nseedzD I DPAM
DC + 1:
(Equation 2)
From this, we see that PAM bias and the base pairing biases all contribute to setting the extent of the seed region (Figures 2A andS2B). Weakening the PAM or correct-match bias extends the seed region, whereas weakening the bias for incorrect matches shrinks it.
After PAM recognition and R-loop formation, cleavage com-pletes a successful targeting process (Figure 1B, right panel). Tuning the final transition state allows us to toggle between different regimes of minimal single-mutation specificity. Targets with a PAM distal mismatch get cleaved with near unity probabil-ity ðpmaxz1Þ only if all transition states toward cleavage
(including the cleavage step) lie well below the transition state to unbinding (Figures 2C, left panel, andS2C). For slow enough enzymatic activity, the final barrier toward cleavage might not go
far below the barrier to unbinding, limiting the maximal cleavage compared to the perfect match (pmax< 1;Figure 2C, right panel).
Consequently, there can be a noticeable effect on off-target ac-tivity also when the mismatch is outside the seed region (Figures 2A andS2C). Reversing this logic implies that pmax< 1 is
indica-tive of a relaindica-tively slow cleavage reaction. Rule (2): Mismatch Spread
Considering more complex mismatch patterns, we start by addressing all possible dinucleotide mismatches (Figures 3A and 4B). The overall cleavage and binding patterns obtained strongly resemble experimental observations (Boyle et al., 2017; Fu et al., 2013, 2014a; Hsu et al., 2013). As expected, placing both mismatches within the seed disrupts cleavage ( Fig-ure 3A). However, moving the mismatches outside the seed does not necessarily restore cleavage activity. With the first mismatch outside the seed region, a second mismatch only abolishes cleavage if it is situated before nseed + npair(Figure 3B), with
npairz
DI
DC+ 1;
(Equation 3)
in the large-bias limit (Experimental Procedures;Supplemental Experimental Procedures 2). The general form of the two-mismatch seed region is shown inFigure 3B, where only off targets in the red region lead to cleavage. In the dark blue region, off targets are rejected due to the first mismatch, and
in the light blue region, they are rejected due to the second mismatch.
The single- and double-mismatch rules can now be unified and generalized (Figure 3D, right panel) into a single rule for any number of mismatches: off targets will typically be rejected if any mismatch, say the m:th mismatch, is positioned closer than nseed + ðm 1Þnpairto the PAM.
Note that, for systems not requiring PAM recognition,
nseed= npair. The above rule also captures the extreme case of
a ‘‘block’’ of B consecutive mismatches, which has also been investigated experimentally (Fu et al., 2013; Hsu et al., 2013; Jo et al., 2015; Singh et al., 2016). Placing such a block effec-tively acts as placing a single mismatch with the bias DIscaled
by the size of the block (Figures 3C, 3D, and S3), giving a block-seed region of size nseed+ ðB 1Þnpair. Hence, a block of
mismatches leads to less off targeting compared to spread out mismatches (Figures 3C and 3D). Given the correspondence of these predictions with literature, our model seems to automati-cally and correctly capture the non-multiplicative cleavage sup-pression by multiple mismatches, in sharp contrast to the ad hoc scoring schemes employed in current prediction algorithms (Haeussler et al., 2016).
Rule (3): Differential Binding versus Differential Cleavage
Catalytically dead systems (for example, dCas9 [Jinek et al., 2012] or Cascade without Cas3) bind strongly to sites that their A
B
C
Figure 2. Rule (1)—Seed Region
(A) The relative-to-WT cleavage probability of a target with a single mismatch. Our model predicts a sigmoidal curve, with maximum off-target activity pmax, seed
length nseed, and width of the seed to non-seed transition 1=DC. SeeFigure S2for parametric sweeps.
(B) Transition landscapes illustrating that the placement of a single mismatch (fltr: before, exactly at, beyond the seed’s border) influences the cleavage probability.
(C) Increasing the kinetic bias against cleavage can suppress cleavage of off targets with a PAM-distal mismatch (compare right panel to right panel in B) while still maintaining a high on-target activity (left panel).
catalytically active counterparts do not cleave (Boyle et al., 2017; Duan et al., 2014; Kuscu et al., 2014; O’Geen et al., 2015; Tsai et al., 2015; Wu et al., 2014). In order to explain this effect, we model inactive systems with a very large cleavage barrier (gray inFigure 1B, right panel;Experimental Procedures). In agree-ment with experiagree-mental observations (Semenova et al., 2011), our model predicts a dissociation constant that is higher when a mismatch is placed closer to the PAM (Figures 4B andS4).
Similar to the cleavage efficiency in the kinetic regime, the dissociation constant takes on a sigmoidal form (Supplemental Experimental Procedures 3). However, this equilibrated seed length (Figure S4) is different from the kinetic counterpart dis-cussed above (Supplemental Experimental Procedures 3). Binding affinities therefore do not need to report on cleavage activity. In general, the gene-editing (Cas9) and gene-silencing (dCas9) capabilities should be seen as two related but separate properties of the RGN. For example, the most stable configura-tion of the RGN on the mismatched target shown in the right panel of Figure 4A is a bound state with a partial R-loop (purple). However, a catalytic active variant will most likely eventually reject this off target (gray), as the barrier to cleavage is higher than to unbinding. Hence, even though cleavage sites are strong binders (Figure 4A, left panel), observing a long bind-ing time on an off-target site should not be taken to imply that this site will also display substantial off-target cleavage (Figure 4A, right panel).
Active Cas9 variants also strongly bind to sites they are incapable of cleaving, especially those containing multiple
PAM-distal mismatches (Bikard et al., 2013; Dahlman et al., 2015). Such a series of mismatches induces a large barrier that opposes, and thereby likely prevents, cleavage ( Fig-ure 4C). Although we are yet to extract temporal information from our model, it is clear that the state right before the first mismatch (purple) might be stably bound over experimental timescales.
Rule (4): Specificity-Efficiency Decoupling PAM Recognition
R-loop formation is preceded by PAM recognition. Although PAM mismatches often completely abolish interactions with the target (Hsu et al., 2013; Semenova et al., 2011; Sternberg et al., 2014), binding to (and interference with) targets flanked by non-canonical PAM sequences has been observed (Leenay et al., 2016). Because PAM mismatches will shift the entire free-energy landscape upward from the bound PAM state on-ward (Figure 1B, left panel), these always increase the highest barrier to cleavage, thereby reducing the cleavage efficiency on any sequence. For increased specificity, we thus need the cleavage efficiency for the off targets to be reduced more than for the target itself.
Protein reengineering approaches most easily affect the overall strength of PAM interactions, influencing the kinetic bias for both the correct PAM ðDPAMÞ and incorrect PAM
ðD0PAMÞ. InFigure 5A, we show the relative cleavage efficiency
between protospacers flaked by incorrect and correct PAMs, and in Figure 5B, we show the cleavage efficiency D
B
A C
Figure 3. Rule (2)—Mismatch Spread
(A) The relative-to-WT probability to cleave a target with two mismatches for a system with DPAM= 3:5 kBT; DI= 4 kBT; DC= 1 kBT; and Dclv= 1 kBT. The seed
length nseedis indicated with dashed lines, and nseed+ npairis indicated with dotted lines.
(B) Schematic of the probability to cleave a target with two mismatches. The target is typically rejected in both blue regions and rejected in the red. (C) Probability to cleave a target with a block of B mismatches as a function of the location of the last mismatch. Also seeFigure S3.
(D) Spreading out blocked mismatches (left panel) around their average position significantly lessens the barrier to cleavage (right panel).
with the correct PAM—both as functions of the average kinetic biasððDPAM+ D
0
PAMÞ=2Þ and the kinetic bias difference
ðDPAM D
0
PAMÞ. As long as the system operates in region A
(Figure 5A), it is possible to increase the specificity by lowering the average kinetic bias toward R-loop initiation without changing the kinetic-bias difference (Supplemental Experi-mental Procedures 2). Outside this region, the system either does not discriminate between PAMs (region C) or is insensi-tive to the average kinetic bias (region B). Interestingly, it is only in region B that lowering the average bias also leads to a lower on-target efficiency (Figure 5B), and consequently, the wild-type (WT) nuclease can only be improved if brought into region A, where it is possible to engineer specificity increases with limited costs in the on-target efficiency. The transition-state diagrams shown in the top panel ofFigure 5C show a situation where the barrier to cleavage (rightmost node) is substantially lower than the barrier to unbinding (left-most node) for two different PAM biases, both resulting in near unit probability to cleave, and corresponding to region C in
Figure 5A. Re-engineering the nuclease to have overall weaker PAM binding (Figure 5C, bottom panel) brings the system into region B, where the cleavage probability for the correct PAM (black) remains close to unity, whereas the probability of cleaving with the incorrect PAM (gray) is drastically lowered. The above scenario might explain how PAM mutant Cas9s are able to outperform their WT counterparts (Kleinstiver et al., 2015a, 2015b) on specificity without significant loss in efficiency.
Sequence Recognition
Another approach to gain specificity is to weaken the protein-DNA interactions affecting the bias for R-loop extension ( Klein-stiver et al., 2016b; Slaymaker et al., 2016). InFigure 5D, we show how engineering the PAM-bound nuclease in this way, inducing a lower gain for correct base pairing, can render previ-ously cleaved off targets (gray line in top panel) rejected (gray line in bottom panel). We further see how we can retain on-target A
B
C
Figure 4. Rule (3)—Differential Binding versus Differential Cleavage
(A) Transition landscapes illustrating the difference between active Cas9 (gray curves) and dCas9 (black curves) when encountering either the cognate site (left panel) or an off target with a mismatch within the seed (right panel).
(B) The dissociation constant for targets with any combination of two mismatches for energetic bia-ses dPAM= 7:5 kBT, dC= 1 kBT, and dI= 8 kBT. The
end of the seed region is indicated with dashed lines. See Figure S4 for single-mismatched off targets.
(C) Transition landscape for an active Cas9 bound to an off-target possessing a block of mismatches placed at the PAM-distal end. Even though cleav-age is unlikely, unbinding takes a long time.
specificity if the highest transition state to-ward cleavage (rightmost node of black line) remains substantially lower than the transition state to unbinding (leftmost node of black line). The above scenario might explain how mutant Cas9s could have an extended seed while having negli-gible reduction in on-target cleavage activity (Kleinstiver et al., 2016b; Slaymaker et al., 2016).
Comparison to Experimental Data for a Broad Class of RNA-Guided Nucleases
To test our model, we acquired published datasets from different RGN systems and fittedEquation 1to singly mismatched targets and blocks of mismatches. The fitted sigmoid has only three effective fit parametersðpmaxor KD; max; nseed; and DCÞ, so we
can unfortunately not get an estimate for all microscopic param-eters from the single-mismatch datasets (Supplemental Experi-mental Procedures 2 and 3)—for this, further experiments are required, as outlined below. Details of the fitting procedure and additional fits can be found inSupplemental Experimental Procedures 4.
Perhaps the best-characterized RGN system is the type II CRISPR-associated Streptococcus Pyogenes Cas9 (spCas9). Among the systems we estimate parameters for, the dataset fromAnderson et al. (2015)traces out the sigmoidal trend partic-ularly well. For this dataset, we fit out a kinetic seed of about 11.3 [11.0,11.4] nt (68% confidence interval between 11.0 and 11.4) and an average bias per correct base pair of about DC= 1:70 ½1:15; 4:0 kBT (Figure 6A). This positive bias indicates
that association with the RGN stabilizes the hybrid, which is in line with recent studies demonstrating that the protein has a strong contribution to the energetics of the resulting bound com-plex (Kleinstiver et al., 2016b; Salomon et al., 2015; Slaymaker et al., 2016). The relative cleavage probability levels off around
pmax= 0:74 [0.72,0.77], indicating that spCas9 retains some
specificity even against errors that are outside the seed. We per-formed additional fits using a second target site from the dataset of Anderson et al. and data obtained from Pattanayak et al. (2013), which produced results that do not significantly differ (Figures S5A–S5C).
Recently, the type V CRISPR-associated enzyme Cpf1 has been characterized as another single-subunit RGN (Zetsche et al., 2015). Kleinstiver et al. (2016a) performed in vivo (human cells) cleavage assays using two different variants named LbCpf1 (Figure 6B) and AsCpf1 (Figure 6C). Both variants exhibit quantitatively similar off targeting, both with seed lengths (nseedz18:9 ½18:5; 19:2 nt for LbCpf1 versus
19:1 ½18:7; 19:3 nt for AsCpf1) and maximum off-target activity (pmaxz0:84½0:66; 1:0 nt for LbCpf1 versus 0:83 ½0:71; 1:0 for
AsCpf1). Compared to spCas9, the Cpf1s are much more spe-cific as the seed region is significantly larger.
Single-molecule fluorescence resonance energy transfer (FRET) experiments done with hAgo2 (Jo et al., 2015) utilized tar-gets with two consecutive mismatches. Given that hybrid forma-tion is not preceded by PAM recogniforma-tion, and that consecutive mismatches impose a combined penalty (Figures 3C and 3D), the estimated half-saturation point is approximately twice the ki-netic seed length for a single mismatch (nseedz10 [9.5,9.9] nt).
The hAgo2 data thus suggest a similar seed length as that of spCas9 (Figure 6D), consistent with the observation that hAgo2 and spCas9 display structural similarities within their respective seed regions (Jiang et al., 2016). Our fits further reveal that hAgo2 likely exhibits a substantially lower gain per correctly formed base pairðDCz0:77 ½0:63; 0:92 kBTÞ.
Unlike the aforementioned RGNs, the type I CRISPR uses a multi-subunit protein complex, termed Cascade, to target in-vaders (Brouns et al., 2008).Semenova et al. (2011)measured the dissociation constant in vitro of the E. coli subtype I-E Cascade. Fitting their data, we find that mismatches within the first 9 nt of the guide lead to rapid rejection (Figure 6E). Interest-A
D B
C Figure 5. Rule (4)—Specificity-Efficiency De-coupling
(A) The cleavage probability on a fully cognate target but with a mismatched PAM, compared to one with the correct PAM, as a function of the average and difference in the kinetic bias of the correct and incorrect PAM. Independent of the sequence following both PAMs, one can identify three regimes (Supplemental Information). Only in regime a is the RGN’s specificity improved through a decrease in the average PAM bias toward R-loop initiation. (B) On-target efficiency for the target with the cor-rect PAM. In regime a, the RGN’s efficiency is not compromised, allowing for simultaneous mainte-nance of on-target efficiency and specificity. (C) The cognate protospacer flanked by either a canonical PAM (black) or incorrect PAM sequence (gray) is bound by a WT (top panel) or engineered RGN (panel).
(D) A matched/mismatched protospacer (black/ gray) bound by WT/engineered RGN (top/bottom panel).
ingly, the energetic gain for a match again suggests a large contribution of the protein to the overall stability (energetic bias dCz3:7 kBT). Structurally, subunits
of the Cascade complex bind to nucleo-tides 6, 12, 18, 24, and 30 of the guide (Zhao et al., 2014). To model this property, we assume that incorporating matches or mismatches at the Cascade-guide binding positions does not affect affinity. Including this effect mainly reduced the estimated energetic gain for matches (dCz1:9 kBT; Supplemental Experimental Procedures 4; Fig-ure S5D), a value more in line to those obtained for the other CRISPR systems.
DISCUSSION
We have presented a general description of target recognition by RGNs with a progressive matching between guide and target (Figure 1A), applicable to both CRISPR and Argonaute systems. In its simplest form, our model contains only two parameters to describe the R-loop formation process: an average kinetic bias toward incorporation beyond a matchðDCÞ and an average
kinetic bias against extending the R-loop beyond a mismatch (DI;
Figure 1B, middle panel). Despite the simplifications going into this minimal model, we can qualitatively understand the targeting rules for these RGNs as resulting from kinetics, as illustrated graphically for seed region (Figure 2B), mismatch spread (Figure 3D), the poor match between cleavage propen-sity and binding propenpropen-sity (Figure 4A), and the specificity-efficiency decoupling (Figures 5C and 5D). Based on our model, we have been able to establish a general targeting rule: off targets will typically be rejected if any mismatch, say the
m:th mismatch, is positioned closer than nseed + ðm 1Þnpairto
the PAM.
AlthoughFigure 6shows that our model can already describe experimental data from various RGNs, the number of microscopic
parameters in the physical model (DPAM, DC, DI, and Dclv;
Fig-ure 1B) exceeds the number of fit parameters available from single-mismatch experimentsðDC; pmax; and nseedÞ. It is
there-fore not possible to determine all the microscopic parameters from single-mismatch experiments alone. However,Figure 3B shows that, with two mismatches, we could also fit out npairand
so determine all the microscopic parameters. It should be possible to directly extract all four microscopic parameters once such extended datasets become available.
One should recognize that our minimal model does not cap-ture all the physics of the targeting process. Nucleic acid interac-tions are explicitly sequence dependent, RGNs are known to undergo conformational changes prior to cleavage (Klein et al., 2017; Sternberg et al., 2015; Xue et al., 2016), and the DCwe
fit out inFigure 6technically only reports the matching bias at the end of the seed, allowing for variable biases along the R-loop. Although these are all topics that need to be explored for future improved quantitative predictions, such extensions are not needed to explain the observed targeting rules and will not qualitatively alter the trends predicted by our model. An exception might be the data from Cpf1 (Figures 6B and 6C), because it shows an increased tolerance to mismatches of nu-cleotides 1, 2, 8, and 9 compared to our minimal model, with a second independent study showing the same behavior (Kim
et al., 2016). Similarly, deviations from the sigmoidal trend are observed for Cascade (Figure 6E). Such features could be ex-plained either through a sequence or position dependence of the kinetic biases.
In conclusion, our model is capable of explaining the observed off-targeting rules of CRISPR and Argonaute systems in simple kinetic terms. After having established the general util-ity of this approach, the next step will be to move beyond our minimal model and gradually allow for conformational control and sequence effects by letting our parameters depend on the nature of matches/mismatches as well as their positions. Fitting such a generalized model against training data would likely improve on present target prediction algorithms by limiting overfitting, as it captures the basic targeting rules deduced from experiments while using only a minimal set of physically meaningful parameters.
EXPERIMENTAL PROCEDURES
A General Model for RGNs with Progressive R-Loop Formation followed by Cleavage
Given the observed dependence of cleavage activity on Cas9 concentration (Cameron et al., 2017; Fu et al., 2013; Kuscu et al., 2014; O’Geen et al., 2015; Pattanayak et al., 2013), we here limit ourselves to the regime where nuclease concentrations are low enough that all binding sites are unsaturated.
A B C
D E
Figure 6. Comparison to Experimental Data
(A–E) Fit of sigmoid (Equation 1) to experimental data from (A) spCas9 (Anderson et al., 2015), (B) LbCpf1 (Kleinstiver et al., 2016a), (C) AsCpf1 (Kleinstiver et al., 2016a), (D) human Argonaute 2 (Jo et al., 2015), and (E) E. coli Cascade complex (Semenova et al., 2011). Values reported in (A)–(D) correspond to the median of 1,000 bootstrap replicates, and the confidence intervals in the text correspond to 68%. SeeFigure S5for additional fits. All experimental data shown corresponds to mean± SD.
The unsaturated regime is also the regime with the highest specificity and should therefore be of particular interest in gene-editing applications.
We define the cleavage efficiency Pclvðs j gÞ as the fraction of binding events
to sequence s that result in cleavage, given the RGN is loaded with guide sequence g. If we in the unsaturated regime assume the binding rate to be in-dependent of sequence, we can express the relative rate of non-target versus target cleavage as
pclvðsjgÞ = Pclvðs j gÞ Pclvðg j gÞ:
(Equation 4)
This relative efficiency is a direct measure of specificity, approaching unity for non-specific targetingðPclvðs j gÞzPclvðg j gÞÞ and zero for specific targeting
ðPclvðs j gÞ Pclvðg j gÞÞ.
In our model, we denote the PAM-bound state as 0 and the subsequent R-loop states by the number of base pairs that are formed in the hybrid. Each of the states n= 1; .; N are taken to transition to state n 1=n + 1 with backward/forward hopping rate kbðnÞ=kfðnÞ (Figure 1A). The ratio between
for-ward and backfor-ward rates sets the relative probability of going forfor-ward and backward from any state and can be parametrized in terms of DðnÞ, the differ-ence in the free-energy barrier between going backward and forward from state n (Figure S1A),
kfðnÞ kbðnÞ= e
DðnÞ: (Equation 5)
Here, we measure energy in units of kBT for notational convenience, and we
will refer to DðnÞ as the bias toward cleavage. The model (Figure 1A) is known as a birth-death process (Nowak, 2006), and the cleavage efficiency is given by the expression (Supplemental Experimental Procedures 1)
PclvðsjgÞ = 1 1+XN n= 0e DTðnÞ; DTðnÞ = Xn m= 0 DðmÞ: (Equation 6)
Here, DTðnÞ represents the free-energy difference between the transition state to solution and the forward transition state from position n (Figures S1A–S1C). For systems like hAgo2, there is no initial PAM binding (Bartel, 2009; Klein et al., 2017), and the sums inEquation 6should omit the PAM stateðn; m = 0Þ.
Building Intuition by Using the Transition Landscape (Large Bias Limit)
Though we will use the exact results ofEquation 7for all calculations, it is use-ful to build intuition for the system by considering the case of large biases. In this limit, the termðsay n = nÞ with the highest transition state dominates the
sum inEquations 6and7(Figures S1A and S1B), and the cleavage efficiency can be approximated as
PclvðsjgÞz
1
1+ eDTðnÞ: (Equation 7)
Based on this, we deduce the rule of thumb that cleavage dominates ðPclv> 1=2Þ if the first state of the transition landscape is the highest
(DTðnÞ > 0;Figure S1A). Conversely, a potential target is likely rejected ðPclv< 1=2Þ if any of the other transition states lies above the first (DTðnÞ < 0;
Figure S1B).
A Minimal Model for RGNs with Progressive R-Loop Formation followed by Cleavage
Given that the defining feature of RGNs is their ability to target any sequence, we expect the major targeting mechanisms to depend more strongly on mismatch position than on the precise nature of the mismatches. With this in mind, we consider a sequence-independent model with the aim of finding a description that captures the gross, sequence-averaged features with a min-imal number of parameters.
Focusing first on how PAM binding effects the system (Figure 1B, left panel), we see that Dð0Þ = DPAMcontrols the kinetic bias between initiating R-loop
for-mation and unbinding. A canonical PAM (black) promotes R-loop initiation, whereas a non-canonical PAM lessens (darker gray) or reverses (lighter gray) the bias toward R-loop formation. Note that PAM-independent systems omit this initial step.
Turning to the bias of R-loop progression, we represent the guide-target hybrid as a sequence of matches (C, correct base pairing) and mismatches (I, incorrect base pairing). Defining the average kinetic bias toward/against extending the R-loop by one correct/incorrect base pair as DC=DI(Figure 1B,
middle panel), we take DðnÞ = DCor DðnÞ = DI, depending on whether the
base pairing is correct or incorrect (Supplemental Experimental Procedures 2). In the middle panel of Figure 1B, we show a transition landscape with moderate gains for correct base pairings and moderate costs for incorrect base pairings (dark gray). The black transition landscape corresponds to an increased gain for matches, whereas the light gray corresponds to an increased penalty for mismatches.
Lastly, considering the bias between cleavage and unwinding of the R-loop, we assume that an incorrect base pair at the terminal position adds the same change in bias as it did in the interior of the R-loop. Therefore, introducing the cleavage bias Dclv, we take DðNÞ = DclvC for a correct match and
DðNÞ = Dclv
I for a mismatch, with DclvC=I= DC=IHDclvas bias against cleavage
from the fully hybridized state (Figure 1B, right panel). In the right panel of Fig-ure 1B, we show examples where the terminal bias Dclv
C=Icorresponds to a
ter-minal match (black), terter-minal mismatch (dark gray), and for a catalytically dead nuclease (light gray).
Dissociation Constant for Catalytically Dead Nucleases
Apart from examining cleavage propensity, many experiments have focused on the binding of catalytically dead Cas9 (dCas9) or other catalytically dead RGNs (Boyle et al., 2017; Josephs et al., 2015; Kuscu et al., 2014; O’Geen et al., 2015; Ran et al., 2015; Semenova et al., 2011; Wu et al., 2014). To be able to relate pure binding experiments to cleavage experiments, we also calculate the dissociation constant KDfor our minimal model when describing
a catalytically dead system (DclvzN;Figure S1D) through
Pbound= ½RGN
½RGN + KD:
(Equation 8)
Here, Pboundequals the probability to bind a substrate in any of the (N) possible
R-loop configurations and follows from Equation 7(Supplemental Experi-mental Procedures 3). Further, [RGN] denotes the concentration of effector complex. Differences in stability of the bound states now parameterize our model (Figure S1D).
SUPPLEMENTAL INFORMATION
Supplemental Information includes Supplemental Experimental Procedures and five figures and can be found with this article online athttps://doi.org/ 10.1016/j.celrep.2018.01.045.
ACKNOWLEDGMENTS
First and foremost, M.D. would like to thank Ralph Seidel for introducing him to the problem of sequential target recognition during a visit to Delft. We would also like to thank Aafke van den Berg, Michiel Bongaerts, and Kristian Blom for fruitful discussion regarding the theoretical modeling. We further acknowl-edge discussions we have had with all members of the CRISPR/microRNA community in Delft: Viktorija Globyt_e, Luuk Loeff, Tao Ju (Thijs) Cui, Stanley Chandradoss, Sungchul Kim, Seung Hwan Lee, Chirlmin Joo, Rebecca McKenzie, Jochem Vink, Sebastian Kieper, and Stan Brouns. M.K. also thanks Iason Katechis for introducing him to the Python fitting library (lmfit) and Re-becca, Thijs, and Chirlmin for carefully reading and commenting on the manu-script. We gratefully thank Emily Anderson, Benjamin Kleinstiver, and Keith Joung; Sungchul Hohng, Soochul Shin, and Myung Hyun Jo; Ekaterina Seme-nova; and Vikram Pattanayak for sharing their data and answering all our ques-tions. This work (M.K.) was supported by the Netherlands Organisation for Scientific Research, as part of the Frontiers in Nanoscience program.
M.D. acknowledges financial support from a TU Delft startup grant. This work (B.E.-M.) forms part of the research program ‘‘Crowd management: the phys-ics of genome processing in complex environments,’’ which is (partly) financed by the Netherlands Organisation for Scientific Research.
AUTHOR CONTRIBUTIONS
M.K. and M.D. designed the research. M.K., B.E.-M., and D.G.A. performed the research and, together with M.D., interpreted the data. M.K., M.D., and B.E.-M. wrote the manuscript.
DECLARATION OF INTERESTS
The authors declare no competing interests.
Received: August 7, 2017 Revised: December 7, 2017 Accepted: January 17, 2018 Published: February 6, 2018
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